I’ve always found timekeeping a little bit fascinating. Since we’re particularly trying to describe how high precision timekeeping should work, and we’re talking about attoseconds precision potentially, let’s consider the following scenario:
I’m in a laboratory on earth. I want to keep track of the passage of time. I wait until my instrument detects some particular pulse of a distant quasar, and my colleagues around the world have all agreed that we will wait for that particular pulse and call this the beginning of our “epoch” or time t = 0. We have extremely precise atomic clocks we can carry around in our pockets because we are superheros with alien tech in this scenario perhaps 
Now, I have two devices listening for that quasar, and they are 1m apart in my lab… but one is 1m closer to the quasar than the other so the second one will receive the pulse about 3.3356 nanoseconds after the other as measured by the one that receives it “first”.
I then take my portable pocket atomic clock accurate to 1 millisecond in a billion years or whatever, go get on an airplane, fly around to my colleagues lab which is on the other side of the earth, but just happens to have been exactly the same distance from the quasar as my first clock at the time of the pulse… Now our atomic clocks should be “synchronized”… but they aren’t! Why? because I traveled at nonzero speed in the airplane! People who travel around experiencing accelerations etc have their clocks run slower. So I arrive at my colleagues lab and the clocks are a few nanoseconds off from each other. My colleague experienced more time than I did!
So by the time we’re talking nanoseconds, much less attoseconds, we need to specify a LOT of things about the measurement scenario before we can compare timestamps to even nanosecond precision. For example which clock is making the measurements and where specifically is it, and what is the gravitational field in the vicinity and what motions is it undergoing etc?
All that being said, a lot of people who have need for nanosecond precision will be taking repeated measures with a “stationary” clock so yeah, that’s probably going to give you a consistent reference frame, unless a train load of gold bullion happens to pass by outside the lab and alter your local gravitational field in the 7th decimal place or something.